than cylindrical sides, otherwise the curved surface of the water will act like a lens and make the drop appear flattened.)

The reason that liquids are not more commonly observed to take the spherical form is that ordinarily the force of gravity is so large as to be more influential in determining their shape than are the cohesive forces. As verification of this statement we have only to observe that as a body of liquid becomes smaller and smaller-that is, as the gravitational forces upon it be

FIG. 94. Spherical globule of oil, freed

from action of gravity

Thus, very small

come less and less-it does indeed tend more and more to take the spherical form. globules of mercury on a table will be found to be almost perfect spheres, and raindrops or minute floating particles of all liquids are quite accurately spherical.

115. Contractility of liquid films; surface tension. The tendency of liquids to assume the smallest possible surface furnishes a simple explanation of the contractility of liquid films.

Let a soap bubble 2 or 3 inches in diameter be blown on the bowl of a pipe and then allowed to stand. It will at once begin to shrink in size and in a few minutes will disappear within the bowl of the pipe.

The liquid of the bubble is simply obeying the tendency to reduce its surface to a minimum, a tendency which is due only to the mutual attractions which its molecules exert upon one another. A candle flame

held opposite the opening in the stem of the pipe will be deflected by the current of air which the contracting bubble is forcing out through the stem.

Again, let a loop of fine thread be tied to a wire ring, as in Fig. 95. Let the ring be dipped into a soap solution so as to form a film across it, and then let a hot wire be thrust through the film inside the loop. The tendency of the film outside the loop to contract will instantly snap out the thread into a perfect circle (Fig. 96). The reason that the thread takes the circular form is that, since the film outside the loop is striving to assume the smallest possible surface, the area inside the loop must of course become as large as possible. The circle is the figure which has the largest possible area for a given perimeter.

Let a soap film be formed across the mouth of a clean 2-inch funnel, as in Fig. 97. The tendency of the film to contract will be sufficient to lift its weight against the force of gravity.

The tendency of a liquid to reduce its exposed surface to a minimum, that is, the tendency of any liquid surface to act like

Fig. 98. Some of the stages through which a slowly forming drop passes

a stretched elastic membrane, is called surface tension. The elastic nature of a film is illustrated in Fig. 98, which is from a motion-picture record of some of the stages through which a slowly forming drop passes.

116. Ascension and depression of liquids in capillary tubes. It was shown in Chapter II that, in general, a liquid stands at the same level in any number of communicating vessels. The following experiments will show that this rule ceases to hold in the case of tubes of small diameter.

Let a series of capillary tubes of diameter varying from 2 mm. to .1 mm. be arranged as in Fig. 99.

When water or ink is poured into the vessel it will be found to rise higher in the tubes than in the vessel, and it will be seen that the smaller the tube the greater the height to which it rises. If the water is replaced by mercury, however, the effects will be found to be just inverted. The mercury is depressed in all the tubes, the depression being greater in proportion as the tube is smaller (Fig. 100, (1)). This depression is most easily observed with a U-tube like that shown in Fig. 100, (2).

Experiments of this sort have established

the following laws:

1. Liquids rise in capillary tubes when they FIG. 99. Rise of are capable of wetting them, but are depressed

in tubes which they do not wet.

liquids in capillary

tubes

2. The elevation in the one case and the depression in the other are inversely proportional to the diameters of the tubes.

It will be noticed, too, that when a liquid rises, its surface within the tube is concave upward, and when it is depressed its surface is convex upward.

(2)

117. Cause of curvature of a liquid surface in a capillary tube. All of the effects presented in the last paragraph can be explained by a consideration of cohesive and adhesive forces. However, throughout the explanation we must keep in mind two familiar facts: first, that the surface of a body of water at rest, for example a pond, is at right angles to the resultant force, that is, gravity, which acts upon it; and, second, that the force of gravity acting on a minute amount of liquid is negligible in comparison with its own cohesive force (see § 114).

Consider, then, a very small body of liquid close to the point o (Fig. 101), where water is in contact with the glass wall of the tube. Let the quantity of liquid considered be so minute that the force of gravity acting upon it may be disregarded. The force of adhesion of the wall will pull the liquid particles at o in the direction oE. The force of cohesion of the liquid

FIG. 101

FIG. 102

will pull these same particles in the direction oF. The resultant of these two pulls on the liquid at o will then be represented by OR (Fig. 101), in accordance with the parallelogram law of Chapter V. If, then, the resultant oR of the adhesive force oE and the cohesive force oF lies to the left of the vertical om (Fig. 102), since the surface of a liquid always assumes a position at right angles to the resultant force, the liquid must rise up against the wall as water does against glass (Fig. 102).

If the cohesive force oF (Fig. 103) is strong in comparison with the adhesive force oE, the resultant oR will fall to the right of the vertical, in which case the liquid must be depressed about o. Whether, then, a liquid will rise against a solid wall or be depressed by it will depend only on the relative strengths of the adhesion of the wall for the liquid and the cohesion of the liquid for itself. Since mercury does not wet glass, we know that cohesion is here relatively strong, and we should expect, therefore, that the mercury

would be depressed, as indeed we find it to be. The fact that water will wet glass indicates that in this case adhesion is relatively strong, and hence we should expect water to rise against the walls of the containing vessel, as in fact it does.

It is clear that a liquid which is depressed near the edge of a vertical solid wall must assume within a tube a surface which is convex upward, while a liquid which rises against a wall must within such a tube be concave upward.

118. Explanation of ascension and depression in capillary tubes. As soon as the curvatures just mentioned are produced, the concave surface aob (Fig. 104) tends, by virtue of

surface tension, to straighten out into the flat surface aob. But it no sooner thus begins to straighten out than adhesion again elevates it at the edges. It will be seen, therefore, that the liquid must continue to rise in the tube until the weight of the volume of liquid lifted, namely amnb (Fig. 105), balances the tendency of the surface aob to flatten out. That the liquid will rise higher in a small tube than in a large one is to be expected, since the weight of the column of liquid to be supported in the small tube is less.

The convex mercury surface aob (Fig. 106) falls until the upward pressure at o, due to the depth h of mercury (Fig. 107), balances the tendency of the surface aob to flatten.